Coherent Frames
Ataollah
Askari Hemmat
Department of Mathematics, Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, P.O.Box 76169-133, Kerman, Iran.
author
Ahmad
Safapour
Department of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, P.O.Box 518, Rafsanjan, Iran.
author
Zohreh
Yazdani Fard
Department of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, P.O.Box 518, Rafsanjan, Iran.
author
text
article
2018
eng
Frames which can be generated by the action of some operators (e.g. translation, dilation, modulation, ...) on a single element $f$ in a Hilbert space, called coherent frames. In this paper, we introduce a class of continuous frames in a Hilbert space $\mathcal{H}$ which is indexed by some locally compact group $G$, equipped with its left Haar measure. These frames are obtained as the orbits of a single element of Hilbert space $\mathcal{H}$ under some unitary representation $\pi$ of $G$ on $\mathcal{H}$. It is interesting that most of important frames are coherent. We investigate canonical dual and combinations of this frames
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
11
v.
1
no.
2018
1
11
http://scma.maragheh.ac.ir/article_32195_afa7e7e72abfe740af573ccc4c15cbac.pdf
dx.doi.org/10.22130/scma.2018.68276.261
On Polar Cones and Differentiability in Reflexive Banach Spaces
Ildar
Sadeqi
Department of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.
author
Sima
Hassankhali
Department of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.
author
text
article
2018
eng
Let $X$ be a Banach space, $C\subset X$ be a closed convex set included in a well-based cone $K$, and also let $\sigma_C$ be the support function which is defined on $C$. In this note, we first study the existence of a bounded base for the cone $K$, then using the obtained results, we find some geometric conditions for the set $C$, so that ${\mathop{\rm int}}(\mathrm{dom} \sigma_C) \neq\emptyset$. The latter is a primary condition for subdifferentiability of the support function $\sigma_C$. Eventually, we study Gateaux differentiability of support function $\sigma_C$ on two sets, the polar cone of $K$ and ${\mathop{\rm int}}(\mathrm{dom} \sigma_C)$.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
11
v.
1
no.
2018
13
23
http://scma.maragheh.ac.ir/article_32215_2e744dde303f4e6c175af724da107e48.pdf
dx.doi.org/10.22130/scma.2018.72221.284
Meir-Keeler Type Contraction Mappings in $c_0$-triangular Fuzzy Metric Spaces
Masoomeh
Hezarjaribi
Department of Mathematics, Payame Noor University, p.o.box.19395-3697, Tehran, Iran.
author
text
article
2018
eng
Proving fixed point theorem in a fuzzy metric space is not possible for Meir-Keeler contractive mapping. For this, we introduce the notion of $c_0$-triangular fuzzy metric space. This new space allows us to prove some fixed point theorems for Meir-Keeler contractive mapping. As some pattern we introduce the class of $\alpha\Delta$-Meir-Keeler contractive and we establish some results of fixed point for such a mapping in the setting of $c_0$-triangular fuzzy metric space. An example is furnished to demonstrate the validity of these obtained results.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
11
v.
1
no.
2018
25
41
http://scma.maragheh.ac.ir/article_31436_7931223a921acacbf9af5f50b37f2216.pdf
dx.doi.org/10.22130/scma.2018.60715.215
On the Integral Representations of Generalized Relative Type and Generalized Relative Weak Type of Entire Functions
Sanjib
Kumar Datta
Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.
author
Tanmay
Biswas
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India.
author
text
article
2018
eng
In this paper we wish to establish the integral representations of generalized relative type and generalized relative weak type as introduced by Datta et al [9]. We also investigate their equivalence relation under some certain conditions.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
11
v.
1
no.
2018
43
63
http://scma.maragheh.ac.ir/article_27953_14efa717fdebe100e756052a42d77176.pdf
dx.doi.org/10.22130/scma.2017.27953
$G$-dual Frames in Hilbert $C^{*}$-module Spaces
Fatemeh
Ghobadzadeh
Department of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.
author
Abbas
Najati
Department of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.
author
text
article
2018
eng
In this paper, we introduce the concept of $g$-dual frames for Hilbert $C^{*}$-modules, and then the properties and stability results of $g$-dual frames are given. A characterization of $g$-dual frames, approximately dual frames and dual frames of a given frame is established. We also give some examples to show that the characterization of $g$-dual frames for Riesz bases in Hilbert spaces is not satisfied in general Hilbert $C^*$-modules.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
11
v.
1
no.
2018
65
79
http://scma.maragheh.ac.ir/article_32196_3364381d248abfc90aba70ebe0afb964.pdf
dx.doi.org/10.22130/scma.2018.74231.310
Some Fixed Point Results for the Generalized $F$-suzuki Type Contractions in $b$-metric Spaces
Sumit
Chandok
School of Mathematics, Thapar University, Patiala-147004, India.
author
Huaping
Huang
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, PR China.
author
Stojan
Radenović
Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, Serbia.
author
text
article
2018
eng
Compared with the previous work, the aim of this paper is to introduce the more general concept of the generalized $F$-Suzuki type contraction mappings in $b$-metric spaces, and to establish some fixed point theorems in the setting of $b$-metric spaces. Our main results unify, complement and generalize the previous works in the existing literature.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
11
v.
1
no.
2018
81
89
http://scma.maragheh.ac.ir/article_31379_085d0dfa121b0af90091cb95f787a50b.pdf
dx.doi.org/10.22130/scma.2018.52976.155
Linear Maps Preserving Invertibility or Spectral Radius on Some $C^{*}$-algebras
Fatemeh
Golfarshchi
Department of Multimedia, Tabriz
Islamic Art University, Tabriz, Iran.
author
Ali Asghar
Khalilzadeh
Department of Mathematics, Sahand University of Technology, Sahand Street, Tabriz, Iran.
author
text
article
2018
eng
Let $A$ be a unital $C^{*}$-algebra which has a faithful state. If $\varphi:A\rightarrow A$ is a unital linear map which is bijective and invertibility preserving or surjective and spectral radius preserving, then $\varphi$ is a Jordan isomorphism. Also, we discuss other types of linear preserver maps on $A$.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
11
v.
1
no.
2018
91
97
http://scma.maragheh.ac.ir/article_23702_316d0365f3c8803a7c76c12c9e348c05.pdf
dx.doi.org/10.22130/scma.2017.23702
A Coupled Random Fixed Point Result With Application in Polish Spaces
Rashwan Ahmed
Rashwan
Department of Mathematics, Faculty of Science, Assuit University, Assuit 71516, Egypt.
author
Hasanen Abuel-Magd
Hammad
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt.
author
text
article
2018
eng
In this paper, we present a new concept of random contraction and prove a coupled random fixed point theorem under this condition which generalizes stochastic Banach contraction principle. Finally, we apply our contraction to obtain a solution of random nonlinear integral equations and we present a numerical example.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
11
v.
1
no.
2018
99
113
http://scma.maragheh.ac.ir/article_28506_00489e0591464d632713e87b210c626a.pdf
dx.doi.org/10.22130/scma.2017.28506
The Integrating Factor Method in Banach Spaces
Josefina
Alvarez
Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003, USA.
author
Carolina
Espinoza-Villalva
Departamento de Matem\'aticas, Universidad de Sonora, Hermosillo, Sonora 83000, Mexico.
author
Martha
Guzman-Partida
Departamento de Matem\'aticas, Universidad de Sonora, Hermosillo, Sonora 83000, Mexico.
author
text
article
2018
eng
The so called integrating factor method, used to find solutions of ordinary differential equations of a certain type, is well known. In this article, we extend it to equations with values in a Banach space. Besides being of interest in itself, this extension will give us the opportunity to touch on a few topics that are not usually found in the relevant literature. Our presentation includes various illustrations of our results.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
11
v.
1
no.
2018
115
132
http://scma.maragheh.ac.ir/article_31559_3d3a29c3ca9569969a1733143533626c.pdf
dx.doi.org/10.22130/scma.2018.63445.240
Identification of Initial Taylor-Maclaurin Coefficients for Generalized Subclasses of Bi-Univalent Functions
Arzu
Akgul
Department of Mathematics, Faculty of Arts and Science, Kocaeli University, Kocaeli, Turkey.
author
text
article
2018
eng
In the present work, the author determines some coefficient bounds for functions in a new class of analytic and bi-univalent functions, which are introduced by using of polylogarithmic functions. The presented results in this paper one the generalization of the recent works of Srivastava et al. [26], Frasin and Aouf [13] and Siregar and Darus [25].
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
11
v.
1
no.
2018
133
143
http://scma.maragheh.ac.ir/article_31813_4b05488564ecc7fb962eff344c90a60f.pdf
dx.doi.org/10.22130/scma.2018.61252.220